Preference relations on actions and criteria in multicriteria decision making

Let A be a finite set of feasible actions which are judged following several criteria. An outranking relation is defined on A by considering preference of the decision maker as a weak order on each criterion and the relation among criteria as a semi-order on the given set of criteria.Several ways of constructing outranking relations have been proposed. One of the most popular, introduced by B. Roy, for instance ELECTRE(s), is based on the use of weights related to criteria. In our approach, the knowledge of weights is replaced by the existence of a semi-order.A case study is developed. It deals with a computer selection problem.     

Multi-criteria decision making with fuzzy linguistic preference relations

Although the analytic hierarchy process (AHP) and the extent analysis method (EAM) of fuzzy AHP are extensively adopted in diverse fields, inconsistency increases as hierarchies of criteria or alternatives increase because AHP and EAM require rather complicated pairwise comparisons amongst elements (attributes or alternatives). Additionally, decision makers normally find that assigning linguistic variables to judgments is simpler and more intuitive than to fixed value judgments. Hence, Wang and Chen proposed fuzzy linguistic preference relations (Fuzzy LinPreRa) to address the above problem. This study adopts Fuzzy LinPreRa to re-examine three numerical examples. The re-examination is intended to compare our results with those obtained in earlier works and to demonstrate the advantages of Fuzzy LinPreRa. This study demonstrates that, in addition to reducing the number of pairwise comparisons, Fuzzy LinPreRa also increases decision making efficiency and accuracy.     

Aggregation of fuzzy preference relations to multicriteria decision making

Weighted aggregation of fuzzy preference relations on the set of alternatives by several criteria in decision-making problems is considered. Pairwise comparisons with respect to importance of the criteria are given in fuzzy preference relation as well. The aggregation procedure uses the composition between each two relations of the alternatives. The membership function of the newly constructed fuzzy preference relation includes t-norms and t-conorms to take into account the relation between the criteria importance. Properties of the composition and new relation, giving a possibility to make a consistent choice or to rank the alternatives, are proved. An illustrative numerical study and comparative examples are presented.     

Approaches to collective decision making with fuzzy preference relations

Recent experimental studies show that the predictive accuracy of many of the solution concepts derived from the collective decision making theory leaves much to be desired. In a previous paper the author attempted to explain some of the inaccuracies in terms of the fuzzy indifference regions of the individuals participating in the voting game. This paper gives straightforward generalizations of the solutions concepts in terms of the fuzzy social or individual preference relations. It turns out that some of these new solution concepts cotain their nonfuzzy counterparts as subsets. Others, in turn, are subsets of their nonfuzzy counterparts. We also discuss a method of aggregating individual nonfuzzy preferences so as to get a fuzzy social preference relation and, furthermore, a nonfuzzy social choice set.     

Extension of VIKOR method for decision making problem based on hesitant fuzzy set

The multiple criteria decision making (MCDM) methods VIKOR and TOPSIS are all based on an aggregating function representing “closeness to the ideal”, which originated in the compromise programming method. The VIKOR method of compromise ranking determines a compromise solution, providing a maximum “group utility” for the “majority” and a minimum of an “individual regret” for the “opponent”, which is an effective tool in multi-criteria decision making, particularly in a situation where the decision maker is not able, or does not know to express his/her preference at the beginning of system design. The TOPSIS method determines a solution with the shortest distance to the ideal solution and the greatest distance from the negative-ideal solution, but it does not consider the relative importance of these distances. And, the hesitant fuzzy set is a very useful tool to deal with uncertainty, which can be accurately and perfectly described in terms of the opinions of decision makers. In this paper, we develop the E-VIKOR method and TOPSIS method to solve the MCDM problems with hesitant fuzzy set information. Firstly, the hesitant fuzzy set information and corresponding concepts are described, and the basic essential of the VIKOR method is introduced. Then, the problem on multiple attribute decision marking is described, and the principles and steps of the proposed E-VIKOR method and TOPSIS method are presented. Finally, a numerical example illustrates an application of the E-VIKOR method, and the result by the TOPSIS method is compared.     

An intuitionistic fuzzy programming method for group decision making with interval-valued fuzzy preference relations

The paper develops a new intuitionistic fuzzy (IF) programming method to solve group decision making (GDM) problems with interval-valued fuzzy preference relations (IVFPRs). An IF programming problem is formulated to derive the priority weights of alternatives in the context of additive consistent IVFPR. In this problem, the additive consistent conditions are viewed as the IF constraints. Considering decision makers’ (DMs’) risk attitudes, three approaches, including the optimistic, pessimistic and neutral approaches, are proposed to solve the constructed IF programming problem. Subsequently, a new consensus index is defined to measure the similarity between DMs according to their individual IVFPRs. Thereby, DMs’ weights are objectively determined using the consensus index. Combining DMs’ weights with the IF program, a corresponding IF programming method is proposed for GDM with IVFPRs. An example of E-Commerce platform selection is analyzed to illustrate the feasibility and effectiveness of the proposed method. Finally, the IF programming method is further extended to the multiplicative consistent IVFPR.     

A rough set approach to intuitionistic fuzzy soft set based decision making

The soft set theory, originally proposed by Molodtsov, can be used as a general mathematical tool for dealing with uncertainty. Since its appearance, there has been some progress concerning practical applications of soft set theory, especially the use of soft sets in decision making. The intuitionistic fuzzy soft set is a combination of an intuitionistic fuzzy set and a soft set. The rough set theory is a powerful tool for dealing with uncertainty, granuality and incompleteness of knowledge in information systems. Using rough set theory, this paper proposes a novel approach to intuitionistic fuzzy soft set based decision making problems. Firstly, by employing an intuitionistic fuzzy relation and a threshold value pair, we define a new rough set model and examine some fundamental properties of this rough set model. Then the concepts of approximate precision and rough degree are given and some basic properties are discussed. Furthermore, we investigate the relationship between intuitionistic fuzzy soft sets and intuitionistic fuzzy relations and present a rough set approach to intuitionistic fuzzy soft set based decision making. Finally, an illustrative example is employed to show the validity of this rough set approach in intuitionistic fuzzy soft set based decision making problems.     

A fuzzy soft set theoretic approach to decision making problems

The problem of decision making in an imprecise environment has found paramount importance in recent years. A novel method of object recognition from an imprecise multiobserver data has been presented here. The method involves construction of a Comparison Table from a fuzzy soft set in a parametric sense for decision making.     

An adjustable approach to fuzzy soft set based decision making

Molodtsov’s soft set theory was originally proposed as a general mathematical tool for dealing with uncertainty. Recently, decision making based on (fuzzy) soft sets has found paramount importance. This paper aims to give deeper insights into decision making based on fuzzy soft sets. We discuss the validity of the Roy-Maji method and show its true limitations. We point out that the choice value designed for the crisp case is no longer fit to solve decision making problems involving fuzzy soft sets. By means of level soft sets, we present an adjustable approach to fuzzy soft set based decision making and give some illustrative examples. Moreover, the weighted fuzzy soft set is introduced and its application to decision making is also investigated.     

Application of fuzzy soft set in decision making problems based on grey theory

There are many uncertain problems in practical production and life which need decisions made with soft sets and fuzzy soft sets. However, the basis of evaluation of the decision method is single and simple, the same decision problem can obtain different results from using a different evaluation basis. In this paper, in order to obtain the right result, we discuss fuzzy soft set decision problems. A new algorithm based on grey relational analysis is presented. The evaluation bases of the new algorithm are multiple. There is more information in a decision result based on multiple evaluation bases, which is more easily accepted and logical to one’s thinking. For the two cases examined, the results show that the new algorithm is efficient for solving decision problems.     

Application of fuzzy soft set in decision making problems based on grey theory

There are many uncertain problems in practical production and life which need decisions made with soft sets and fuzzy soft sets. However, the basis of evaluation of the decision method is single and simple, the same decision problem can obtain different results from using a different evaluation basis. In this paper, in order to obtain the right result, we discuss fuzzy soft set decision problems. A new algorithm based on grey relational analysis is presented. The evaluation bases of the new algorithm are multiple. There is more information in a decision result based on multiple evaluation bases, which is more easily accepted and logical to one’s thinking. For the two cases examined, the results show that the new algorithm is efficient for solving decision problems.     

A robust additive consistency-based method for decision making with triangular fuzzy reciprocal preference relations

To express uncertain information in decision making, triangular fuzzy reciprocal preference relations (TFRPRs) might be adopted by decision makers. Considering consistency of this type of preference relations, this paper defines a new additive consistency concept, which can be seen as an extension of that for reciprocal preference relations. Then, a simple method to calculate the triangular fuzzy priority weight vector is introduced. When TFRPRs are inconsistent, a linear goal programming framework to derive the completely additive consistent TFRPRs is provided. Meanwhile, an improved linear goal programming model is constructed to estimate the missing values in an incomplete TFRPR that can address the situation where ignored objects exist. After that, an algorithm for decision making with TFRPRs is presented. Finally, numerical examples and comparison analysis are offered.     

An integrated multiple criteria decision making model applying axiomatic fuzzy set theory

This article presents a hybrid model for the multiple criteria decision making problems. The proposed decision model consists of three parts: (i) DEA (data envelopment analysis) is used to provide the best combination on the performance parameters of original data; (ii) By the application of AFS (axiomatic fuzzy set) theory and AHP (analytic hierarchy process) method, the weight of each attribute is calculated and (iii) TOPSIS (technique for order preference by similarity to ideal solution) is applied to provide the ranking order of that best combination based on the weights of attributes. In addition, we also provide the definitely semantic interpretations for the decision results by AFS theory. Specially, the model not only employs the performance parameters from raw data, but also considers the preferences from decision-makers that can make the decision results more reasonable. The proposed model is used for robot selection to verify the proposed model. Using the selection index, the evaluation of alternative robots and the selection of the most appropriate are eventually feasible. Moreover, a numerical example for supplier selection is included to illustrate the application of the model for the newly developed problems.     

A goal programming approach to group decision making based on multiplicative preference relations and fuzzy preference relations

This paper analyses the mechanisms through which binding finance constraints can induce debt-constrained firms to improve technical efficiency to guarantee positive profits. This hypothesis is tested on a sample of firms belonging to the Italian manufacturing. Technical efficiency scores are computed by estimating parametric production frontiers using the one stage approach as in Battese and Coelli [Battese, G., Coelli, T., 1995. A model for technical efficiency effects in a stochastic frontier production function for panel data. Empirical Economics 20, 325–332]. The results support the hypothesis that a restriction in the availability of financial resources can affect positively efficiency.     

A novel approach to interval-valued intuitionistic fuzzy soft set based decision making

The soft set theory, originally proposed by Molodtsov, can be used as a general mathematical tool for dealing with uncertainty. The interval-valued intuitionistic fuzzy soft set is a combination of an interval-valued intuitionistic fuzzy set and a soft set. The aim of this paper is to investigate the decision making based on interval-valued intuitionistic fuzzy soft sets. By means of level soft sets, we develop an adjustable approach to interval-valued intuitionistic fuzzy soft sets based decision making and some numerical examples are provided to illustrate the developed approach. Furthermore, we also define the concept of the weighted interval-valued intuitionistic fuzzy soft set and apply it to decision making.     

A mathematical basis for satisficing decision making

This paper presents a conceptual and mathematical model of the process of satisficing decision making under multiple objectives in which the information about decision maker's preferences is expressed in the form of aspiration levels. The mathematical concept of a value (utility) function is modified to describe satisficing behavior; the modified value function (achievement scalarizing function) should possess the properties of order preservation and order approximation. It is shown that the mathematical basis formed using aspiration levels and achievement scalarizing functions can be used not only for satisficing decision making but also for Pareto optimization, and thus provides an alternative to approaches based on weighting coefficients or typical value functions. This mathematical basis, which can also be regarded as a generalization of the goal programming approach in multiobjective optimization, suggests pragmatic approaches to many problems in multiobjective analysis.     

Logarithmic least squares method to priority for group decision making with incomplete fuzzy preference relations

The aim of this paper is to present a logarithmic least squares method (LLSM) to priority for group decision making with incomplete fuzzy preference relations. We give a reasonable definition of multiplicative consistent for incomplete fuzzy preference relation. We develop the acceptable fuzzy consistency ratio (FCR for short), which is simple and similar to Saaty’s consistency ratio CR for multiplicative fuzzy preference relations. We also extend the LLSM method to the case of individual preference relation with complete information. Finally, some examples are illustrated to show that our method is simple, efficient, and can be performed on computer easily.     

Comment on “A fuzzy soft set theoretic approach to decision making problems”

The algorithm for identification of an object in a previous paper of A.R. Roy et al. [A.R. Roy, P.K. Maji, A fuzzy soft set theoretic approach to decision making problems, J. Comput. Appl. Math. 203(2007) 412–418] is incorrect. Using the algorithm the right choice cannot be obtained in general. The problem is illustrated by a counter-example.     

Group decision making with a fuzzy linguistic majority

The determination of solutions in group decision making is considered. The point of departure is a collection of individual fuzzy preference relations. A solution is derived either directly from the individual fuzzy preference relations or by constructing first a social fuzzy preference relation. As opposed to conventional approaches in which a crisp (threshold type) majority rule is used, we employ a fuzzy majority rule specified by a fuzzy linguistic quantifier, e.g., ‘most’, ‘much more than 50%’, etc. A calculus of linguistically quantified propositions is applied. Using the fuzzy majority, various solution concepts are derived, mainly of the type of core, minimax (opposition) set and consensus winner.     

Hesitant fuzzy Bonferroni means for multi-criteria decision making

Due to the desirable characteristic of the Bonferroni mean (BM) that it can capture the interrelationship between input arguments, and in order to provide the properties and the modelling capability of the BMs under hesitant fuzzy environment, we explore some new hesitant fuzzy Bonferroni means (HFBMs). The properties and the special cases of HFBMs are studied in detail. We specially define a concept of hesitant Bonferroni element (HBE), which is considered as a ‘bonding satisfaction’ factor used as a calculation unit in the HFBM. The HBE can reflect the correlation between hesitant fuzzy arguments, which makes the HFBM have particular advantages in aggregating arguments. In addition, the weighted hesitant fuzzy Bonferroni mean (WHFBM) is also proposed considering different importance degrees of input arguments. Furthermore, the procedure of multi-criteria decision making based on the WHFBM is given under hesitant fuzzy environment as typical applications, which has much sense in theory and practice for the BM.